Nested texture on all sides of cube
The Checker texture is 3D. It divides the given texture space into blocks. The Brick texture is 2D. It's calculated in U and V, but just projected through W. 

So you can map the checker in a 3D space, (here, Object space) but the bricks need some kind of mapping onto 2D surfaces to look like bricks. The default UV map of a cube will do, here.



If you'd like some kind of procedural mapping that rotates the brick texture to line up with surfaces without an explicit UV map, you can use an approach something like this one